It's not impossible, but it's difficult if the doors are different sizes and have different spacing. There are a lot of design compromises.

Here's an article about it (why Vancouver can't have PEDs): https://dailyhive.com/vancouver/translink-skytrain-station-p...

This is not really a big issue for London, though. The vast majority of London Underground platforms only have one type of train serving them. The few exceptions (eg: parts of the Piccadilly and Bakerloo lines) are mostly above ground and not the busiest parts of the network, so you could just skip the PEDs there and use manual door closing.